solve the following quadratic equation using square roots: (x+6)^2/2 = 8
To solve the equation using square roots, we first need to isolate the squared term on one side of the equation.
1. Multiply both sides of the equation by 2 to eliminate the fraction:
(x+6)^2 = 16
2. Take the square root of both sides of the equation to remove the squared term:
√(x+6)^2 = ±√16
3. Simplify the square root of the squared term:
(x+6) = ±4
4. Solve for x:
x+6 = 4 or x+6 = -4
For x+6 = 4:
Subtract 6 from both sides:
x = 4 - 6
x = -2
For x+6 = -4:
Subtract 6 from both sides:
x = -4 - 6
x = -10
Therefore, the solutions to the quadratic equation (x+6)^2/2 = 8 are x = -2 and x = -10.